Keywords

1 Introduction

The production process of concrete consumes abundant resources, it is known that 1700–2000 kg of sand and stone and 350–450 kg of cement will be consumed for 1 m3 of concrete [1]. According to the National Bureau of Statistics, the consumption of sand and stone and cement in 2019 for China is 3.58 billion tons 810 million tons. Sand, stone, and calcium carbonate mineral (main material of cement) are natural resources. The sustained consumption of those natural resources will damage the environment and exhausted the resource, even although China is a rich resource country.

Geopolymer recycled aggregate concrete (GRAC) was prepared by substituting cement with geopolymer and coarse aggregate with recycled aggregate concrete (RAC). GRAC is a green and environmentally friendly building material [2], not only reducing the consumption of natural resources, such as stone and calcium carbonate mineral [3], but also recycling industrial waste such as slag and fly ash [4]. However, due to the difference of the nature of cement to geopolymer and RAC to natural aggregate, some performances of GRAC, such as its size conversion coefficient and size effect, are uncertain. Moreover, because the raw material of geopolymer are different by each researcher, it is hard to give a uniform law to describe the effect of raw material to the properties of GRAC. Therefor, in this study, oxide molar ratio of raw material is selected as the main factor, and its effect on the performance of GRAC is studied.

2 Experimental Program

2.1 Raw Materials

Blast furnace slag used in the test is produced by Anshan Iron and Steel Co.Ltd and a first grade fly ash of Benxi is selected, the main chemical components of which are shown in Table 1. Water glass used is produced by Shandong Yousuo Chemical Technology Co.Ltd. The original modulus is 3.3, the chemical composition of which is shown in Table 2. Recycled aggregate with original strength grade of C40 is used as coarse aggregate, which is artificially broke into a maximum particle size of 25 mm and continuous gradation. Natural medium-fine river sand is used as fine aggregate.

Table 1. Chemical composition of mineral slag and fly ash/wt%
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Table 2. Chemical composition of water glass
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2.2 Experimental Method and Instrument

According to the previous research [5], the optimal alkali-activator solution is used, of which the content of water glass in alkaline activator solution is 40% to the total mass of liquid, and the concentration of NaOH is 9mol/L, liquid binder ratio is 0.5. Sand coarse aggregate ratio is 0.44. Oxide molar ratio (n(CaO):n(SiO2 + Al2O3)) is the main research variable in this research, the value is selected as 0.7, 0.75, 08, 0.85, 0.9. The mixing ratio of each group are shown in Table 3.

GRAC was prepared into cube samples with side lengths of 70 mm, 100 mm, 150 mm and 200 mm. A total of 6 samples of each size and proportion were made, and a total of 120 samples were tested. The compressive strength value and compressive strength test instrument use the RGM-100A microcomputer-controlled universal testing machine produced by Shenzhen Regal Instrument.

Table 3. Mix ratio of GRAC/kg\( \cdot \)m−3
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3 Results and Discussion

3.1 The Influence of Oxide Molar Ratio on Compressive Strength

Figure 1 presents compressive strength under different oxide molar ratio and size.It can be observed that with the increasing of n(CaO):n(SiO2 + Al2O3), the compressive strength of GRAC shows a trend of increases at beginning and then decreases. According to the research of J. L. Provis [6], geopolymers are divided into tow system: N-A-S-H (low or no calcium, three-dimensional network structure) and C-A-S-H (high-calcium, layered structure). The diagrammatic drawings of low-CaO and high-CaO structure are shown in Fig. 2.

As n(CaO): n(SiO2 + Al2O3) increased from 0.7 to 0.8, the structure of geopolymer binder transfers from low-calcium system to high-calcium system. Moreover, according to the research of Wang Qing [7], when the molar ratio exceeds 0.8, the CaO in the system is saturated, then the strength is controlled by the molar ratio of n(SiO2):n(Al2O3). For C-A-S-H structure, as n(SiO2):n(Al2O3) increases from 3 to 4, the strength decreases. Becaease this process is converted from PSS type ([-Si-Al-Si-]) geopolymer to PSSS type ([-Si-Al-Si-Si-]) geopolymer, and the structure of PSS-geopolymer is more dense [8].

The law of the size of the test block on the compressive strength of GRAC is: f100  >  f150  >  f200  >  f70. The general rule is that the larger the side length of the cube test block, the greater the compressive strength. However, the strength of GRAC cube specimen with a side length of 70 mm does not conform to this law, and its compressive strength is the lowest. This is because there are a great deal of original cracks in the recycled aggregate, and as the size of the test block is close to the size of the aggregate, the strength of the concrete will be affected by the cracks more significantly [9].

Fig. 1.
figure 1

Compressive strength under different oxide molar ratio and dimensions

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Fig. 2.
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Low-CaO and High-CaO structure of geopolymer

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3.2 The Influence of Oxide Molar Ratio on Size Conversion Coefficient

Through the size conversion factor (α), compressive strength of non-standard test block can be calculated by the standard specimen. The cube specimen with a side length of 150 mm is a standard specimen, and the conversion coefficients of other non-standard samples are shown in Eqs. (1)–(3):

$$ \alpha_{{{70}}} = f_{{cu,70}} /f_{{cu,150}} $$
(1)
$$ \alpha_{{{100}}} = f_{{cu,100}} /f_{{cu,150}} $$
(2)
$$ \alpha_{{{200}}} = f_{{cu,200}} /f_{{cu,150}} $$
(3)

Figure 3 shows effect of the oxide molar ratio on the size conversion coefficient. It can be seen from Fig. 3 that there are only 2 test data is in the region of 0.95–1.05. That indicates that the size conversion coefficient of GRAC cannot current adopt the value form the national standard “Standard for Test Methods for Mechanical Properties of Ordinary Concrete” GB/T50081, in which the value is 0.95 and 1.05 for samples that size are 100 mm3 and 200 mm3. In this paper, the mathematical equations of oxide molar ratio (ε) and size conversion coefficient (α) are established by the linear fitting. As shown in Fig. 4 and the results are as: a70 = 0.463 + 0.28ε, a100 = 1.016 + 0.12ε, a200 = 0.966–0.04ε.

Fig. 3.
figure 3

Effect of the oxide molar ratio on size conversion coefficient

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Fig. 4.
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Fitting curve of the oxide mole ratio on size conversion coefficient

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3.3 Bazant Size Effect Fitting

GRAC is a kind of quasi-brittle material. The strain energy released by crack propagation under load causes the existence of size effect. According to the size effect theory of Bazant [10], the relationship between the nominal compressive strength of concrete and the size D is shown in Eq. (4)

$$ f_{N} = f_{\infty } (1 + \frac{{D_{b} }}{D}) $$
(4)

In the equation, f∞ is the nominal compressive strength of the infinite size of GRAC, and Db is the effective thickness of the boundary layer cracking. After decomposition:

$$ f_{N} = f_{\infty } + f_{\infty } \times \frac{{D_{b} }}{D} $$
(5)

As X=1/D,\(\text{Y} = f_{N}\), \(\text{C} = f_{\infty }\), \(\text{A} = f_{\infty } \times \text{D}_{\text{b}}\), then Eq. (5) can become a linear equation as shown in Eq. (6)

$$ \text{Y} = \text{AX} + \text{C} $$
(6)
Table 4. Parameter calculation of the theoretical formula of the dimension effect
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Fig. 5.
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Comparison diagram of the measured strength value and the Bazant theoretical strength

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Fig. 6.
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Comparison diagram of dimensionless strength and Bazant theoretical strength

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X and Y can be directly calculated by the strength and the size of the specimen. Table 4 shows parameter calculation of the theoretical equation of the size effect. Through the study of compressive strength and size effect degree (Δa), it is found that the data of the 70 mm cube specimen does not conform to this law, so its data is not used in the calculation.

Figure 5 presents the comparison diagram of measured strength values of cube specimen with different side lengths and the Bazant theoretical strength. It can be seen that under different oxide molar ratio conditions, the measured strength values of compressive strength are all on the theoretical curve, so Bazant theory can be used for GRAC.

3.4 Critical Size and Critical Strength

None-dimensionalized the value of size effect of GRAC [10], shown in Eq. (7), in which \(f_{150}\) is the measured strength of the GRAC in a cube specimen with a side length of 150 mm, and b is the undetermined coefficient of the equation. Then the undetermined coefficients of none-dimensionalized of size effect of GRAC were be worked out by regression analysis of Eq. (6), shown in Eq. (8). The comparison diagram of none-dimensionalized strength and Bazant theoretical strength is shown in Fig. 6,

$$ \frac{{f_{N} }}{{f_{150} }} = \frac{{f_{\infty } }}{{f_{150} }}(1 + \frac{\text{b}}{D}) $$
(7)
$$ \frac{{f_{N} }}{{f_{150} }} = 0.7623 \times (1 + \frac{{{44}{.8486}}}{D}) \;\quad R^2 = 0.85$$
(8)

It can be seen from Fig. 6 that as the side length of the cube specimen is 200 mm, the data of each oxide molar ratio is close to the theoretical curve. The oxide molar ratio of 0.8 is the demarcation point of the size effect change, and its compressive strength is the highest, and the strength will be reduced if it is greater or less than the strength. Therefore, a piece-wise function is used to fit the relationship between oxide molar ratio (ε) and f∞/f150 and Db. Figure 7 shows schematic diagram of the relationship between the oxide molar ratio and f∞/f150 and Db. Equations (9)–(12) are the fitting curve equation.

When 0.7 ≤ ε ≤ 0.8:

$$ \frac{{f_{\infty } }}{{f_{150} }} = {2}.24027{ - }{1}{.}{97934} \times\upvarepsilon $$
(9)
$$ \text{D}_{\text{b}} = { - }347.09643 + 531.1485 \times\upvarepsilon $$
(10)

When 0.8 ≤ ε ≤ 0.9:

$$ \frac{{f_{\infty } }}{{f_{150} }} = { - }0.62015 + 1.59552 \times\upvarepsilon $$
(11)
$$ \text{D}_{\text{b}} = 431.98236{ - }442.4970 \times\upvarepsilon $$
(12)

According to Eqs. (9) to Eq. (12), piece-wise function has higher applicability to oxide mole ratio, and substitute it into Eq. (8). In summary, the predictive equation of the nominal compressive strength of the size effect rate of the compressive strength of GRAC can be obtained by the coupling effect of the size effect and the molar ratio of oxides. As shown in Eq. (13) and Eq. (14).

When 0 ≤ ε ≤ 50%:

$$ \frac{{f_{N} }}{{f_{150} }} = 2.24027{ - }{1}{.97934} \times \upvarepsilon \times (1 + \frac{{{ - }347.09643 + {5}31.1485 \times\upvarepsilon }}{D}) $$
(13)
$$ \frac{{f_{N} }}{{f_{150} }} = { - }0.62015 + 1.59552 \times \upvarepsilon \times (1 + \frac{{431.98236{ - }442.4970 \times\upvarepsilon }}{D}) $$
(14)

According to Eq. (13) and Eq. (14), the critical strength characteristic value (fcr) can be calculated under the condition of different oxide molar ratios and the side length of the specimen is infinite. Consider the scope of application of engineering size effect, when the difference between the nominal compressive strength and the characteristic value of the critical dimension is within 5%, the size of the specimen corresponding to the nominal compressive strength can be considered as the critical dimension (Dcr). Figure 8 presents relationship of the oxide molar ratio to the critical strength and the critical size. It can be seen that as the molar ratio of oxide increases, its critical size gradually increases. However, the critical strength reached its maximum value when the oxide molar ratio was 0.8.The prediction equations proposed by Eq. (13) and Eq. (14) have wider applicability mainly reflected in two aspects: Considering effect of the amount of recycled aggregate and the size effect coupling, so it has higher applicability. The use of dimensionless methods has certain reference significance for predicting the compressive strength of GRAC with other strength grades and oxide molar ratios.

Fig. 7.
figure 7

Relation of the oxide molar ratio to f∞/f150 and Db

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Fig. 8.
figure 8

Relationship of the oxide molar ratio to the critical strength and the critical size

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4 Conclusions

The strength of GRAC increases first and then decreases with the increase in the molar ratio of oxides, and reaches the maximum when n(CaO):n(SiO2 + Al2O3) = 0.8. The law of compressive strength under specimen of different sizes is as follows: f100 > f150 > f200 > f70.

The size conversion coefficient α can be obtained by linear fitting to the relationship between the oxide molar ratio ε.

The compressive strength of the cube specimen with side lengths of 200 mm, 150 mm and 100 mm are in line with Bazant’s theoretical curve of size effect. The non-dimensional method can be used to obtain the prediction equation of the combined effect of the compressive strength of GRAC with the oxide molar ratio and the size effect. Finally, the critical size and critical strength values of GRAC under different oxide molar ratios are obtained.